Cancelled trains in the north of England have cost businesses nearly £38m so far this summer, according to an analysis.

The claim came as Northern Rail reintroduced on Monday three-quarters of the 168 services that were removed from its timetable on 4 June. The remaining 25% will be reintroduced in September.

On Sunday, dozens of trains were cancelled because of staffing shortages, including nearly every service between Liverpool and Manchester airport, leaving many passengers stranded.

Northern, the private train operator behind the cancellations, told passengers the service cuts would ensure “trains are in the right depots ready for the Monday morning commuter services, as we reintroduce most of our May 2018 timetabled services which were suspended on 4 June”.

More than 9,000 Northern rail services were cut from the train schedule over the past two months following the timetable change. The entire Lakes line was closed, prompting a heritage rail company to step into the breach and offer a free service during the run-up to the holiday season.

Sunday’s chaos prompted Andy Burnham, the mayor of Greater Manchester, to write to Theresa May to intervene. He said the transport secretary, Chris Grayling, had broken a promise to make tackling Northern rail issues a top priority.

“There are only so many times that I can call on Chris Grayling to do his job and help rail passengers in the north. He has failed to deliver on his promise to make sorting out rail chaos here his top priority and that is why I feel have no choice but to ask the prime minister to intervene.

Speaking on Monday on BBC Radio 4’s Today programme, Burnham said he was struggling to see why Grayling was still in his job.

He said: “We’ve been saying these services are not working, there is a fundamental problem here, and the response is nothing. He doesn’t come here, he cancelled a conference recently – a northern transport summit – it’s just good not enough.”

Analysis from the Northern Powerhouse Partnership (NPP), a thinktank set up by the former chancellor George Osborne, found £38m had been lost to the northern English economy on Northern trains alone this summer, and up to £1.3m a day at the height of the crisis. It also revealed up to 1m hours of timehad been lost from people’s lives.

Henri Murison, director of NPP, said the economic damage was not “just a flash in the pan but actually will have a longer-term impact, sadly”.

He told BBC Breakfast: “And when this investment which has caused this problem was supposed to have improved things, actually it will have made it worse in the end.”

Jonathan Reynolds, the Labour MP for Stalybridge and Hyde, which has been severely affected by the temporary timetable, said: “Every week I get three or four messages from people who are late for work, people who are in trouble at work for being consistently late, and parents who’ve seen less of their children. It is hard to express just how disillusioned people are with the situation as it stands.”

Northern services on routes in Lancashire, Cumbria and Greater Manchester have been disrupted for months because of delays to electrification of the line between Manchester and Blackpool, and hundreds of trains were cancelled following the implementation of new timetables in May. On Monday, 75% of Northern’s train services will be reinstated.

Bosses had initially promised the full timetable would be reinstated by the end of July, but agreed to a phased reintroduction after discussions with the Rail North Partnership (RNP), which manages the north of England franchises on behalf of the Department for Transport and Transport for the North.

The shadow transport secretary, Andy McDonald, said: “This government is allowing the train operator to get away with it by not holding them to account. Once again the north is an afterthought for this government on transport. It’s time Arriva was stripped of its contract.”

So far, 4,000 monthly and annual pass holders in the worst-affected areas have applied for a refund of four weeks’ worth of travel costs, and the payments would be made this week, a Northern spokesman said.

The full cost to the north of England is likely to be considerably higher than the figures in the report, because the region’s other major rail operator, TransPennine Express, did not provide figures for its affected services between 20 May and the end of June.

Half of trains were significantly delayed or cancelled on some TransPennine routes on some days this summer, according to the NPP analysis.

The NPP’s Devolving Our Railways report says the government must devolve full powers of oversight to Transport for the North to prevent a repeat of the summer’s chaos.

Osborne said: “This report sets out a clear message to government, the Northern powerhouse is crying out for more devolution. This is the very role we envisaged Transport for the North doing when we set them up. Northern leaders will support them in making sure the people of the Northern powerhouse get the modern, connected network they deserve.”